%% Saturn
warning off
clc;clear;
format longg
options_negx = odeset('RelTol',1e-13,'AbsTol',1e-13,'Events',@NegXcrossing);
options=odeset('RelTol',1e-13,'AbsTol',1e-13);
options_fmincon = optimoptions('fmincon', 'MaxFunctionEvaluations', 5000, ...
    'MaxIterations', 5000,'ConstraintTolerance',1e-6,'Algorithm','Interior-point','stepTolerance',1e-21);
%% Inputs.
G           = 6.674e-11 * ((1/1000)^3); % Gravitational parameters

mass_central = 1.989e30;
%[] Mass of central planet

mass_moon = 5.972e24;         %Callisto
%[] mass of moons

DU = 151.73e6;           %Callisto
%[km] Semi-major axis of Moons, used as distance units for each CRTBP
%environment.

moonName = {'Luna'};
%[] Name of the Moons

thetao = 0;
%[] Initial position of the moon relative to the first point of aries

GM_central = mass_central*G;
%[] Gravitational parameters

GM_moon = mass_moon*G;
%[] Gravitational parameters

N = length(mass_moon);
%[] Number of Moons

u = zeros(N,1);
for ii = 1:N
    u(ii) = GM_moon(ii)/(GM_moon(ii)+GM_central);
end
%[] Gravataional ratio

TU = zeros(N,1);
VU = zeros(N,1);
for ii = 1:N
    TU(ii) = sqrt(DU(ii)^3/GM_central);
    VU(ii) = DU(ii)/TU(ii);
end
%[] Time constant for each crtbp system

theta_dot = zeros(1,N);
for ii = 1:length(theta_dot)
    theta_dot(ii) = sqrt(GM_central*DU(ii))/DU(ii)^2;
end
%[] Theta dot for each planet.

planetNumb = 1;
[L1,L2,L3,L4,L5] = librationPoints(u(planetNumb));
L_ = [L1,L2,L3,L4,L5];
for ii = 1:length(L_)
    L_pos = L_(:,ii);
    J_L(ii) = jacobiConst(L_pos,zeros(3,1),u(planetNumb));
end

%%
OpenCRTBP_u(u)
%[] open plot
set(gcf,'color','k')


load('SE_L4_L5_Lyapunov.mat');
%
for ii = 1:length(T)
    to = [0,T(ii)];
    Xo = IC_L4(:,ii);
    [t,S] = ode113(@(t,S)CR3BP_n(t,S,u),to,Xo,options);
    S = S';
    plot3(S(1,:),S(2,:),S(3,:))

end
set(gca,'xcolor','w')
set(gca,'ycolor','w')
set(gca,'zcolor','w')
set(gca,'color','k')

load('SE_L4_Vertical.mat');
%
for ii = 1:length(T_L4_VL)
    to = [0,T_L4_VL(ii)];
    Xo = IC_L4_VL(:,ii);
    [t,S] = ode113(@(t,S)CR3BP_n(t,S,u),to,Xo,options);
    S = S';
    plot3(S(1,:),S(2,:),S(3,:))
end

for ii = 1:length(T_L4_VL)
    Jacobi_Save(ii) = jacobiConst(IC_L4_VL(1:3,ii),IC_L4_VL(4:6,ii),u);
    to = [0,T_L4_VL(ii)];
    Xo = IC_L4_VL(:,ii);
    [t,S] = ode113(@(t,S)CR3BP_n(t,S,u),to,Xo,options);
    S = S';
    for jj = 1:length(S)
        S_i = C2I_new(S(:,jj),u,DU,VU,t(jj));
        COE(:,jj) = State2Coe(S_i,GM_central);
    end

    SMA_max(ii) = max(COE(1,:));
    SMA_min(ii) = min(COE(1,:));
    e_max(ii) = max(COE(2,:));
    e_min(ii) = min(COE(2,:));
    i_max(ii) = max(COE(3,:));
    i_min(ii) = min(COE(3,:));
    clear COE
end
figure;
subplot(3,1,1);
hold on
for ii = 1:length(SMA_min);
    plot(Jacobi_Save(ii),SMA_max(ii),'ro')
    plot(Jacobi_Save(ii),SMA_min(ii),'rd')
end
ylabel('SMA [km]')
set(gca,"FontSize",20)

subplot(3,1,2);
hold on
for ii = 1:length(SMA_min)
    plot(Jacobi_Save(ii),e_max(ii),'ro')
    plot(Jacobi_Save(ii),e_min(ii),'rd')
end
ylabel('Eccentricity')
set(gca,"FontSize",20)

subplot(3,1,3);
hold on
for ii = 1:length(SMA_min)
    plot(Jacobi_Save(ii),i_max(ii),'ro')
    plot(Jacobi_Save(ii),i_min(ii),'rd')
end
ylabel('Inclination [deg]')
xlabel('Jacobi Integral')
set(gca,"FontSize",20)